Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mathcalculus

  • 2 years ago

related rate problem: help please. (attached)

  • This Question is Closed
  1. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

  2. SithsAndGiggles
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Recall the distance formula: \[d^2=(x-x_0)^2+(y-y_0)^2\] In this particular problem, you have \((x_0,y_0)=(0,0)\) (the origin), since you want to find the distance between any given point on the curve \((x,y)\) and the origin. \[d^2=x^2+y^2\] Substitute the given equation of the curve: \[d^2=x^2+\left(4\sqrt{2x+2}\right)^2\\ d^2=x^2+16(2x+2)\\ d^2=x^2+32x+32\] Now differentiate both sides implicitly with respect to some dummy variable \(t\): \[2d\frac{dd}{dt}=(2x+32)\frac{dx}{dt}\] You're told that at the point \((1,8)\), \(x\) is increasing at a rate of 3 units/s, which translates to \(\dfrac{dx}{dt}=3\). \[2d\frac{dd}{dt}=(2\cdot1+32)(3)\\ 2d\frac{dd}{dt}=102\] You're asked to find \(\dfrac{dd}{dt}\), so first you need to find \(d\). To do this, find the distance between \((1,8)\) and \((0,0)\), then plug it into the above equation. Lastly, solve for \(\dfrac{dd}{dt}\).

  3. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @SithsAndGiggles omg thank you!! :)

  4. SithsAndGiggles
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Yer welkum

  5. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @SithsAndGiggles hey, i found the distance which is 8 right? then i plugged in 8 into the equation and got 51/8... however, something is wrong?

  6. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i get \(\frac{19}{8}\)

  7. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh nvm i got it.

  8. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it's 6.32577

  9. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    to find the distance is this:

  10. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i got it... thank you! @satellite73

  11. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[d^2=x^2+32x+32\] \[2dd'=2xx'+32x'\] \[dd'=xx'+32x'\] \[8d'=3+96\]

  12. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh right doh

  13. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    distance isn't 8 is it? distance is \(\sqrt{65}\)

  14. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    which is pretty close to 8...

  15. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  16. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is the final answer \(\frac{99}{\sqrt{65}}\) ?

  17. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    close yes... i thought i had to do this: x2-x1/y2-y1

  18. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it's 51/sqrt(65)/65

  19. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh damn i forgot to divide 32 by 2 must be past my bedtime

  20. mathcalculus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lol

  21. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.